A277437 Square array read by antidiagonals upwards in which T(n,k) is the n-th number j such that, descending by the main diagonal of the pyramid described in A245092, the height difference between the level j (starting from the top) and the level of the next terrace is equal to k.

1, 3, 2, 5, 4, 9, 7, 6, 12, 20, 8, 10, 21, 36, 72, 11, 13, 25, 50, 91, 144, 14, 16, 32, 56, 112

Offset: 1

Author

Omar E. Pol, Dec 29 2016

Keywords

• nonn
• tabl
• more

Comments

This is a permutation of the natural numbers.

Column k lists the numbers with precipice k. For more information about the precipices see A280223 and A280295.

The structure of the stepped pyramid arises after the 90-degree-zig-zag folding of the diagram of the isosceles triangle A237593.

The terraces at the m-th level of the pyramid are also the parts of the symmetric representation of sigma(m), m >= 1.

The stepped pyramid is also one of the 3D-quadrants of the stepped pyramid described in A244050.

If a number m is in the column k and k > 1 then m + 1 is the column k - 1.

The largest Dyck path of the symmetric representations of next k - 1 positive integers greater than T(n,k) shares the middle point of the largest Dyck path of the symmetric representation of sigma(T(n,k)). For more information see A237593.

Examples

			The corner of the square array begins:
   1,  2,  9, 20, 72, 144,
   3,  4, 12, 36, 91,
   5,  6, 21, 50,
   7, 10, 25,
   8, 13,
  11,
  ...
T(1,6) = 144 because it is the smallest number with precipice 6.
		

Links

• Omar E. Pol, Perspective view of the pyramid (first 16 levels)
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Row 1 gives A280295.

Column 1 gives A276112.

Cf. A000203, A071562, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A240542, A244050, A245092, A259179, A262626, A279286, A279385, A280223.

Formula

T(n,1) = A071562(n+1) - 1.

Extensions

a(20)-a(26) from Omar E. Pol, Jan 02 2017